Potential biological applications using triple helical polynucleotides primarily depend upon sequence specificity and high affinity, both of which are essentially thermodynamic properties. A complete thermodynamic characterization of the ATT, ATU and AUU deoxyribonucleotide triplexes has been carried out. This includes their phase diagrams as a function of temperature and salt concentration and the differences in their stability (free energy), enthalpy, entropy and heat capacity. Associated with the melting of homopolynucleotide DNA duplexes, three previously unrecognized features have been found: that helix dissociation is accompanied by a negative heat capacity change that is primarily dependent upon salt concentration, that the value of the enthalpy change divided by the square of the melting temperature is not constant but decreases with increasing salt concentration and that the melting temperature is a cubic function of the sodium chloride activity. Consequently, the changes in the parameter usually interpreted as the number of sodium counterions released upon helix dissociation decreases as a quadratic function of ionic strength and thus is not constant or approximately constant as commonly thought. The observed dependence of the duplex melting temperature upon salt concentration can be quantitatively accounted for by a thermodynamic analysis which indicates that there is a significant interaction of the salt component with the single DNA strands and that in addition to the simple electrostatic interactions of the salt with the charged phosphate groups of the double helix, that there are additional interactions between the salt component and the double helix. As a possible example of such additional interactions, recent computer simulations have reported appreciable accumulation of sodium ions in the vicinity of the O-4 oxygen atoms of the thymine groups of DNA.